131 I-MIBG is a norepinephrine analog that is concentrated in adrenergic tissues and therefore holds promise for cell-specific treatment of neuroblastoma, a lethal childhood tumor. The overall aim of this study is to determine the safety and efficacy of this targeted radioisotope for treatment of neuroblastoma. The study will test the hypothesis that targeted radiotherapy with 131 I-MIBG will produce responses in refractory neuroblastoma; and the major dose-limiting toxicity of 131 I-MIBG will be hematologic, it will be cumulative with successive doses, and can be managed by bone marrow or peripheral blood stem cell re-infusion.